Bifurcations of rough heteroclinic loop with two saddle points

Yinlai JIN
2003 Science in China Series A  
The bifurcation problems of rough 2-point-loop are studied for the case where −ρ 1 i < 0 and λ 1 i > 0 are the pair of principal eigenvalues of unperturbed system at saddle point p i , i = 1, 2. Under the transversal and nontwisted conditions, the authors obtain some results of the existence of one 1periodic orbit, one 1-periodic and one 1-homoclinic orbit, two 1-periodic orbits and one 2-fold 1-periodic orbit. Moreover, the bifurcation surfaces and the existence regions are given.
doi:10.1360/03ys9047 fatcat:yhjqm6swurgf5mkmndhxojakam